Solution of the basic boundary value problems for a degenerate elliptic equation by the method of potentials

R. M. Askhatov^a, R. N. Abaydullin<sup>b

a</sup> Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia
^b Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: Fundamental solutions to a degenerate elliptic equation are found. Using these fundamental solutions, simple and double layer potentials are built. The basic boundary value problems for a degenerate elliptic equation are reduced to the equivalent Fredholm integral equations of the second kind. Their solvability is proved.

Keywords: degenerate elliptic equation, method of potentials, double layer potential, simple layer potential, Fredholm equation, generalized translation operator.

UDC: 517.95

Received: 15.12.2014

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